Defining wavelength

1. Wavelength is the distance from one point on a wave to the equivalent point on the next wave.
2. Two points are equivalent when they are at exactly the same stage of their oscillation, with the same displacement and moving in the same direction.
3. Crest to crest and trough to trough are the easiest equivalent pairs to spot, but any matching pair gives the same distance.
4. The symbol for wavelength is $\lambda$ and its SI unit is the metre, $m$.
5. Short wavelengths are often given in centimetres, where $1cm=0.01m$, or in millimetres, where $1mm=0.001m$.
6. Wavelength is a property of the wave in space, so it describes how stretched out the wave pattern is.

Measuring wavelength

1. Measuring a single wavelength with a ruler gives a large percentage uncertainty, because one wavelength is short compared with the smallest division on the ruler.
2. A more accurate method is to measure the distance across several complete waves and divide by the number of waves.
3. Count the gaps between crests rather than the crests themselves, because five crests in a row mark out only four wavelengths.
4. For example, if six crests span $30cm$, they mark out five wavelengths, so each wavelength is $30÷5=6.0cm$.
5. The distance must be measured along the direction in which the wave is travelling, not across it.

Defining frequency

1. Frequency is the number of complete waves passing a point each second.
2. This is the same as the number of complete oscillations each point makes per second, because every wave that passes makes the point go through one oscillation.
3. The symbol for frequency is $f$ and its unit is the hertz, $Hz$, where $1Hz$ means one complete wave per second.
4. Large frequencies are written with prefixes: $1kHz=1000Hz$, $1MHz=1000000Hz$ and $1GHz=1000000000Hz$.
5. Middle C on a piano has a frequency of about $262Hz$, so the piano string vibrates 262 times every second.
6. The frequency of a wave is fixed by the source that makes it, so it does not depend on the size of the waves.
7. Frequency is a property of the wave in time, so it describes how often the pattern repeats rather than how stretched out it is.
8. A louder sound from the same source has a larger amplitude but the same frequency, because the source is still vibrating at the same rate.

Measuring frequency

1. To find a frequency, pick a fixed point, such as a mark on the side of a ripple tank, and count the complete waves that pass it in a measured time.
2. Divide the number of complete waves by the time in seconds, so 24 waves in $8.0s$ gives a frequency of $3.0Hz$.
3. Counting over a longer time, such as $10s$ rather than $1s$, reduces the effect of your reaction time when starting and stopping the stopwatch.
4. If the period $T$ is known instead, the frequency is found from $f=\frac{1}{T}$.
5. Sound waves have frequencies far too high to count by eye, so they are measured electronically, for example with a microphone connected to a data logger.